Certificate for #5394 ⟨a, b, c | ab=a, bcbc=c⟩

Completion settings:

• Reduction order:
  • Left-to-right shortlex with a < b < c

Axiom: ab=a.

Defines rule #1.

Referenced by [3], [5].

Axiom: bcbc=c.

Referenced by [3], [4], [6].

Overlap of [1] ab=a with [2] bcbc=c:

Critical pair: ac=acbc.

Flip LHS and RHS.

Referenced by [5].

Overlap of [2] bcbc=c with [2] bcbc=c:

Critical pair: bcc=cbc.

Flip LHS and RHS.

Defines rule #3.

Referenced by [5], [6].

Simplify [3] acbc=ac.

Reduce LHS:

Defines rule #2.

Overlap of [2] bcbc=c with [4] cbc=bcc:

Critical pair: bbcc=c.

Defines rule #4.